It is known that the removal of slag from the cutting grove during flame cutting is a limiting factor where cutting speed is concerned. Higher cutting speeds are an advantage with many applications. Thus the cutting speed during autogenic flame cutting of continuous casting ingots is lower than the pull out speed of the ingots. For example, the cutting speed with ingots 200 mm thick amounts to about 0.5 m/min. The pull out speed, on the other hand, amounts to 1.5/2.0 m/min. If the continuous casting ingots are to be cut longitudinally, it is desirable to adapt the cutting speed to the pull out speed.